Related papers: The Kakeya conjecture, after Wang and Zahl

In this paper we give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all dimensions using sophisticated, powerful techniques from a…

We provide an alternative and self contained proof of the main result of Bennett, Carbery, Tao regarding the multilinear restriction estimate. The approach is inspired by the recent result of Guth about the Kakeya version of multilinear…

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

We give a combinatorial proof of the skew Kostka analogue of the K-saturation theorem. More precisely, for any positive integer k, we give an explicit injection from the set of skew semistandard Young tableaux with skew shape…

We consider the transcendental motive of three K3 surfaces $X$ conjectured to have complex multiplication (CM). Under this assumption, we match these to explicit algebraic Hecke quasi-characters $\psi_X$, and CM abelian threefolds $A$. This…

We prove a conjecture of Rudnick and Sarnak on the mass equidistribution of Hecke eigenforms. This builds upon independent work of the authors see arxiv.org:math/0809.1640 and arxiv.org:math/0809.1635.

In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C^*-algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the…

First, we study constructible subsets of $\A^n_k$ which contain a line in any direction. We classify the smallest such subsets in $\A^3$ of the type $R\cup\{g\neq 0\},$ where $g\in k[x_1,...,x_n]$ is irreducible of degree $d$, and $R\subset…

We give a survey on the developments in a certain theory of quantum vertex algebras, including a conceptual construction of quantum vertex algebras and their modules and a connection of double Yangians and Zamolodchikov-Faddeev algebras…

We study a class of q-analogues of multiple zeta values given by certain formal q-series with rational coefficients. After introducing a notion of weight and depth for these q-analogues of multiple zeta values we present dimension…

In this paper, we verify a part of the Mirror Symmetry Conjecture for Schoen's Calabi-Yau 3-fold, which is a special complete intersection in a toric variety. We calculate a part of the prepotential of the A-model Yukawa couplings of the…

We adapt Guth's polynomial partitioning argument for the Fourier restriction problem to the context of the Kakeya problem. By writing out the induction argument as a recursive algorithm, additional multiscale geometric information is made…

Kakeya sets are compact subsets of $\mathbb{R}^n$ that contain a unit line segment pointing in every direction. The Kakeya conjecture states that such sets must have Hausdorff dimension $n$. The property of stickiness was first discovered…

We propose an algebraic geometry framework for the Kakeya problem. We conjecture that for any polynomials $f,g\in\F_{q_0}[x,y]$ and any $\F_q/\F_{q_0}$, the image of the map $\F_q^3\to\F_q^3$ given by $(s,x,y)\mapsto…

Bilinear restriction estimates have been appeared in work of Bourgain, Klainerman, and Machedon. In this paper we develop the theory of these estimates (together with the analogues for Kakeya estimates). As a consequence we improve the…

Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.

The convergence of a sequence of Cauchy sequences is conjectured; which if shown to be true, would prove the Riemann hypothesis by way of LeClair and Fran\c{c}a's transcendental equation criteria.

This document collects several approaches attempted in proving the Chen-Raspaud Conjecture for k = 3. Each approach is detailed with full proofs and explanations of why it failed. This compilation aims to provide insights and a foundation…

A two-dimensional Besicovitch set over a finite field is a subset of the finite plane containing a line in each direction. In this paper, we conjecture a sharp lower bound for the size of such a subset and prove some results toward this…

The goal of the paper is twofold: it aims to give an extensive set of tools and bibliography towards Nowicki's conjecture both in an associative setting; it establishes a new result about Nowicki's conjecture for the free metabelian Poisson…